Model for Earthquake on a Tall Building

This is a rough model of the behavior of an idealized tall building undergoing horizontal seismic motion. The building has floors supported by walls. (Each floor has mass but the weight is not taken into account.) The displacements of the floors from their equilibrium positions are , , …, ; initially these displacements and their velocities are set to zero. Each floor experiences a restoring forces from its contiguous floors according to Hooke's law with a spring constant . The diagonal lines represent shock absorbers that introduce a damping factor .